Page:Proceedings of the Royal Society of London Vol 1.djvu/498

Rh the theory of atoms by which these facts are explained is by no means of importance to the present inquiry. It is by means of a series of numbers computed according to the method of Richter, that this scale is constructed so as to answer at one view the very numerous questions that occur to an analytic chemist in the examination of any saline compouud. It is similar in principle to the common sliding rule, and like that instrument has the usual Gunter's line of numbers on the slider; but upon a line adjacent to the slider are marked certain points corresponding to those numbers which represent the various chemical elements, acids, alkalies, and other compounds intended to be included in the present view. By motion of the slider any one point of the line of numbers, as 100, may be made to correspond with the point indicating any compound, as sulphate of potash. By the position of the point for sulphuric acid, this salt is seen to contain 46 of acid, and the other ingredient potash at the same time corresponds with 54 on the slider. By the position of the point for sulphate of barytes, it appears that 135 of this precipitate would be obtained from 100 of the salt, and in the same manner that it would yield 176 of sulphate of lead, with a great variety of similar answers respecting the equivalent quantities of other compounds in which the same quantiﬁes of acid or neutralizing base is contained.

Since the line of numbers is so divided that a given space of every part of it corresponds to numbers that bear a given ratio to each other, and since the intervals on the adjacent column of equivalents are all laid down according to certain given portions of the same scale, they directly indicate by juxtaposition numbers that are in the same proportion on any part of the scale that may be presented to them, as will be very evident to those who are acquainted with the common properties of other sliding rules.

For the sake of those who may not be accustomed to the use of the sliding rule, and for the purpose of recommending that valuable instrument to more general use, the author enters rather more than might otherwise he requisite into the elementary principles of logometric division.

In a paper communicated to the Royal Irish Academy by Dr. Mooney, the method of exterminating any number of quadratic surds is pointed out by successively squaring them when brought alone to one side of the equation; and the present is an extension of the same method : ﬁrst, to all surds whose indices are any integral power of 2, as the fourth, eighth, sixteenth, thirty-second power, &c.; and next to cubic surds, and to any number of surds whose common indices are in any manner compounded of the factors 2 and 3; next